function RBF_NN_Example()

clc

clear all

%??創建訓練樣本

%??線性函數的訓練

Mn_Train=100*[rand(1,5) rand(1,5)+0.5 rand(1,5)+1 rand(1,5)+1.5;...

rand(1,5) rand(1,5)+0.5 rand(1,5)+1 rand(1,5)+1.5];

n=size(Mn_Train,2);

%??Mn_Train 為2*20的矩陣

Nn_Train=[2*Mn_Train;3*Mn_Train(1,:)];

%??Nn_Train 為3*20的矩陣

%??將訓練樣本進行聚類分析,分為4類

H=4;

%??將樣本歸一化

[SampleX,pmin,pmax,SampleY,tmin,tmax]=premnmx(Mn_Train,Nn_Train);

%??將訓練樣本進行聚類并形成聚類中心

options=statset('Display','final');

[index,center]=kmeans(SampleX',H,'Distance','city',...

'Replicates',10,'Options',options);

figure(1)

X=SampleX';

set(figure(1),'color','w')

hold on

plot(X(index==1,1),X(index==1,2),'ro','markersize',9,'markeredgecolor',...

'k','markerfacecolor','r')

plot(X(index==2,1),X(index==2,2),'go','markersize',9,'markeredgecolor',...

'k','markerfacecolor','g')

plot(X(index==3,1),X(index==3,2),'mo','markersize',9,'markeredgecolor',...

'k','markerfacecolor','m')

plot(X(index==4,1),X(index==4,2),'bo','markersize',9,'markeredgecolor',...

'k','markerfacecolor','b')

plot(center(:,1),center(:,2),'ko','markersize',15,'markeredgecolor',...

'k','markerfacecolor','k')

title('樣本聚類','fontsize',16)

grid on

hold off

%??spread徑函數的擴展速度設置

spread=0.3;

%??基于高斯函數的隱藏層神經元的輸出

%??形成4*20的矩陣

%??閾值

b=ones(1,H)*0.8326/spread;

center=center';

Hidden_Out=zeros(H,size(SampleX,2));

for i=1:H

for j=1:size(SampleX,2)

Hidden_Out(i,j)=exp(-b(i)*(norm(SampleX(:,j)-center(:,i)).^2));

end

end

%??對輸出層權重的訓練,最速下降法

MaxIteration=1000;

Iteration=0;

tol=1e-3;

lemda=0.001;

%??初始化參數和閾值

N=size(SampleY,1);

W=0.5*rand(N,H)-0.1;

B=0.5*rand(N,1)-0.1;

%??網絡輸出值

NetOut=W*Hidden_Out+repmat(B,1,n);

Resid=SampleY-NetOut;

%??均方誤

MSE_error=sumsqr(Resid)./(N*n);

%??訓練權重開始

while Iteration

NetOut=W*Hidden_Out+repmat(B,1,n);

Resid=SampleY-NetOut;

MSE_error=sumsqr(Resid)./(N*n);

Delta=Resid;

%??最速下降訓練

dW=Delta*Hidden_Out';

dB=Delta*ones(n,1);

W=W+lemda*dW;

B=B+lemda*dB;

if MSE_error

break;

end

Iteration=Iteration+1;

end

NetOut=W*Hidden_Out+repmat(B,1,n);

Samplefit=postmnmx(NetOut,tmin,tmax);

%??將擬合樣本和原樣本比較

figure(2)

set(figure(2),'color','w')

hold on

subplot(3,1,1)

hold on

plot(1:20,Nn_Train(1,:),'ro-','markersize',8)

plot(1:20,Samplefit(1,:),'bo-','markersize',8)

title('樣本擬合對比')

subplot(3,1,2)

hold on

plot(1:20,Nn_Train(2,:),'ro-','markersize',8)

plot(1:20,Samplefit(2,:),'bo-','markersize',8)

title('樣本擬合對比')

subplot(3,1,3)

hold on

plot(1:20,Nn_Train(3,:),'ro-','markersize',8)

plot(1:20,Samplefit(3,:),'bo-','markersize',8)

title('樣本擬合對比')

hold off

總結

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